Hamiltonian formulation of Wilson's lattice gauge theories

1975/01/15 by John B. Kogut, Leonard Susskind · 2 voices · 42 citations
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies

paper · doi:10.1103/physrevd.11.395

openalex publication_date 1975/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Wilson's lattice gauge model is presented as a canonical Hamiltonian theory. The structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators. The gauge-invariant configuration space consists of a collection of strings with quarks at their ends. The strings are lines of non-Abelian electric flux. In the strong-coupling limit the dynamics is best described in terms of these strings. Quark confinement is a result of the inability to break a string without producing a pair.

Citations

• On the Self-Energy and the Electromagnetic Field of the Electron
• Conservation of Isotopic Spin and Isotopic Gauge Invariance

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Discussions

• Reading https://doi.org/10.1103/PhysRevD.11.395.. . The paper can only be found without a paywall using certain websites... [[from comments]: but it’s behind a paywall.] As an initial note, the above- [stackexchange, 3 points]
• Reading Hamiltonian formulation of Wilson's lattice gauge theories , I found that in discretizing the Hamiltonian, the following continuous to discrete map is done: $$ -i \bar \psi \gamma^i\partial_i [stackexchange, 3 points]

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